DE2354562A1 - METHOD FOR DETERMINING AN OPTICALLY ISOTROPIC REFLECTION ARRANGEMENT AND IN PARTICULAR OPTICAL REFLECTION ARRANGEMENT WITH ISOTROPIC ANGLE REFLECTION, DETERMINED BY SUCH A METHOD - Google Patents

Description

Patent attorney

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nU ütomsciüifstr. 10

310-21.61.4P October 31, 1973

SOCIETE D ¹ OPTIQUE, PRECISION ELECTRONIQUE ET MECANIQUE
- SOPELEM, Paris (France)

Method for determining an optically isotropic reflection arrangement and in particular according to such a method
certain optical reflection arrangement with isotropic
oblique reflection

The invention relates to a method for determining an optically isotropic reflection arrangement, which with polarized light in an extended Spectral range should work with good correction of the phase anisotropy and has at least one metallic mirror, which may be covered with a thin layer of a transparent dielectric

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310- {72/98) -DF-R (12) _-; -

and to which an equivalent crystalline compensation layer is assigned, as well as on reflection arrangements with isotropic oblique Reflections that can be determined in particular using such a method.

The aim of the invention is a method for determining an optical Reflection arrangement that is within an extended spectral range shows no influence on the polarization state of an obliquely incident light wave, or one with the help of such a method obtained optical reflection arrangement with isotropic oblique reflection.

The invention can be used in particular in all optical devices that operate with polarized light, in which To save space, a bent beam guide is provided for the polarized light. This is especially true with polarized Optical microscopes of modern design working in light, cases in which it is advantageous between objective and Ocular auxiliary systems such as zoom systems or pupillary relays to insert into the beam path of light without itself

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thereby increasing the height of the corresponding .optischen device. So far, however, it has proven impossible to guide the light beams on a kinked path without causing a disturbance in the polarization state of the incident light waves.

It is well known that every oblique reflection is a polarized one Light wave on a metallic surface in an anisotropic manner. This is due to an inequality of the reflection coefficients, that for light polarized parallel to the plane of incidence (polarization state p) or for light polarized perpendicular to the plane of incidence light (polarization to stand s) apply · These reflection coefficients are in the general case complex, expressions of the form

i * p ~
re ^J ', and they can be both in its modulus and in its P r Phase ¹ differ from one another, of the moduli Inequality .führt z'u a rotation of the polarization direction of the incident light, and therefore, they can be achieved by a corresponding rotation of the Compensate the polarizer. The inequality in the phases, on the other hand, leads to the conversion of an incident linear oscillation into a reflected elliptical oscillation. Because both inequalities

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are present at the same time corresponds to an incident linearly polarized one Wave is an elliptically polarized reflected wave, the large one being The axis of the polarization ellipse does not match the direction of the linear one Polarization of the incident wave coincides.

In practice, this phase anisotropy makes two things impossible:

On the one hand, between two polarizers arranged on either side of a mirror with any orientation with crossed polarizers Transmission direction No complete light extinction obtained, 'and secondly, the birefringence of one arranged in front of a mirror Object cannot be measured using compensation.

Various partial solutions are now known for this problem. Sp, for example, a first mirror in its effects compensate by using a mirror that is identical to it, the planes of incidence for the light running perpendicular to each other in both mirrors must «The Liehtwaves polarized parallel to the plane of incidence for the first mirror then show one to the plane of incidence of the second Mirror's perpendicular polarization direction and vice versa; this from

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CAPDECOMME specified solution, however, has the disadvantage of a considerable complication of the overall optical Scheraas, and it cannot always be reconciled with the available space.

Furthermore, a crystalline λ / 2 plate can be placed between two mirrors that work under the same conditions Insert a way that the light waves polarized parallel and perpendicular to the plane of incidence experience a mutual exchange « In this case, however, an effective compensation can: only be achieved for a single light frequency, namely the frequency for which the λ / 2 plate is exactly half a wavelength thick. It is therefore impossible to use this method with light waves, light composed of different wavelengths and, in particular, -with white light, this solution, like the previous one, also has the disadvantage "that it has two mirrors or at least an even number of mirrors required.

Even a prism with total reflection is not a perfect solution; Although it has no amplitude anisotropy, it

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however shows a considerable phase anisotropy which is approximately constant over the entire spectrum of visible light, for example for glass with a refractive index of 1.6 is 51.

It is now known to compensate for the phase anisotropy of any mirror or prism with total reflection for a specific wavelength by means of a compensator with birefringence. However, such a compensation also does not apply to an extended spectral range and in particular not to white light. This is particularly the case with the usual mirrors made of aluminum, which for their protection are covered with a layer of silicon dioxide with a thickness of the order of magnitude of 1000 Å. In the table shown in FIG. 1, the phase anisotropy occurring in degrees for such a mirror at an angle of incidence of 45 for the entire spectrum of visible light is given in the first line. In order to obtain a phase anisotropy of zero in the middle of the spectrum, a quartz plate with a thickness of 60 microns must be used as a compensator, which brings about a birefringence of 360 for this wavelength.

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In the table in Fig. 1 igt again in the second line. in degrees the phase anisotropy given by such a quartz plate marriage depending on the wavelength over the entire spectral = " The third line of the table in FIG. 1 then contains the remaining during compensation ending residual, i.e. the phase difference that occurs after the light beam is reflected on the mirror and passed through the quartz plate remains. The in this line of the table of Fig. 1 an = given data show that with the help of a double fraction ^ den! Compensators actually compensate only in one way narrow spectral range can be achieved in the middle of the spectrum; to both sides of this middle wavelength range, the phase deviation even greater than it is without observing the compensation, the same phenomenon also shows when an exact phase correction for a different wavelength than that medium wavelength is tried

The invention is therefore based on the object of showing a way in which a reflection arrangement can be obtained, in which one or more mirrors have a birefringent grain

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pensator is assigned and the sufficient phase compensation for polarized light in an extended spectral range and in particular in the entire spectrum of visible light.

This object is <invention achieved on the basis of a method of the type mentioned above characterized in that the thickness of the dielectric layer of the or the mirror and the thickness of the crystalline for a given angle of incidence! Compensating layer a as a function of the other determined by the First the variation of the phase difference between the complex reflection coefficient of the mirror or mirrors for light polarized parallel and perpendicular to the plane of incidence with different thicknesses of the dielectric depending on the wavelength in the respective spectral range, second the variation of the two polarization directions from the The phase difference resulting from the passage of the light through the physicalization layer for different thicknesses of the compensation layer as a function of the same wavelengths and finally the variation of the residual in the compensation of the phase differences as a function of the same wavelength for j every pair is determined from a compensation layer.

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ter thickness and a mirror dielectric of a certain thickness calculated in such a way that the respective phase differences for the mean Wavelength of the relevant spectral range to each other in absolute value equal and opposite in sign, and the final selection of the thickness pair taking into account the minimum thickness for the dielectric compatible with the mechanical strength of the mirror than the predominant one Factor or taking into account the compensation residual when the mirrors used have appropriate thicknesses for the dielectric allow-

The invention also relates to a reflection arrangement with isotropic oblique reflection with at least one, possibly with one thin layer of a transparent dielectric coated metallic mirror, which is a crystalline mirror equivalent to a thin layer Kpmpensationssc is not assigned, the thickness of the dielectric Layer of the mirror or mirrors and the thickness of the crystalline compensation layer according to the method mentioned above can be determined. Exist with such a reflection arrangement the mirror or mirrors made of aluminum and (lie-crystalline grains

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The dielectric layer is made of quartz or magnesium fluoride Layer preferably has an optical thickness of less than 600 A. In the case of optical reflection arrangements designed according to the invention for an isotropic oblique reflection for incident below 45 white polarized light can be an uncoated mirror made of aluminum with an equivalent compensation layer Quartz with a thickness of 2.2 microns or with an equivalent compensation layer made of magnesium fluoride with a thickness of 1.7 microns can be combined.

To further illustrate the invention and the advantages that can be achieved, four special exemplary embodiments are now intended will be described in detail.

It should first be remembered that for a metallic Mirror, which is covered with a dielectric layer for its protection, for the incident light with the polarization state ρ The corresponding reflection coefficient can be expressed by the formula:

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¹¹ - 23S4BS2

whereby:

r, (rp or rs) is the modulus of the complex reflection coefficient ' for the polarization state ρ or s is ^

ψ ( ip or ^ s) denotes the phase of the complex reflection coefficient for the polarization state ρ or s,

rl, (rip or rls) the real coefficient of the r-layer for the

Polarization state is ρ or s,

r2, (r or r, the modulus of the complex reflection coefficient

the metal layer for the polarization state ρ or s is

cC, (öCp or fits) the phase of the complex reflection coefficient

The metal layer for the polarization state ρ or s denotes and

β = 4% - ^ iilcös i 1 for the wavelength λ and a layer thickness d applies * Furthermore, as is well known, the following relationships apply:

■ tq (io _f H) r2 = tg (il r J2)

^IP ~ tg (io - il) ^P tg (il Φ il)

_1ς sinÜo - il) ■ ■ ■ _& sin Ul - i2)

sin (io + il) sin (il + i2)

where io is the angle of incidence,

il is the angle of refraction in the dielectric layer and 92 denotes the complex angle of refraction in the metal;

4.09823 / Ö? 2ä ...

These different angles are due to the relationships

no Sin io = nlSin il = n2 Sin i2 connected to each other, where

no the real refractive index in air, nl the real refractive index in the dielectric layer and n2 = η - jk denote the complex refractive index in the metal.

It should also be noted that the complex refractive index n2 = η - jk in a metal such as aluminum or silver is not absolutely constant Size is, but can vary quite considerably depending on the type of formation of the metal layer. For those given below Embodiments have the refractive index for aluminum and for silver as indicated in the table of FIG Values.

If the angle of incidence io and the optical parameters for the metal and the dielectric layer are known, the phase * fp and the phase ψ s corresponding to the polarization states can therefore be used for a given layer thickness and a given wavelength

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get ρ and s and derive the phase difference "fp -» fs from this, which is introduced by the reflection on the mirror. In this way a family of curves can be obtained which show the phase differences depending on the different wavelengths of the spectral range under consideration and for different thicknesses of the dielectric Play layer.

In the graphical representation of FIG. 3, such a network of curves for a mirror made of aluminum is shown in solid lines. shown at an angle of incidence of 45 from a ray white polarized light is hit. The different curves of this network correspond to different thicknesses for the protective layer of silicon dioxide, which vary from an initial value of zero (uncoated mirror) to a final value of 1020 A, where this last layer thickness corresponds to a value customary in practice for mirrors provided with a protective layer.

It should also be remembered that the phase anisotropy A Ψ introduced by a crystalline layer can be expressed by the formula:

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Af = 2 ξ (N - N)
A 2 ο

in the D for the thickness of the crystal layer, Λ for the wavelength of the incident light, N for the extraordinary index of refraction of the crystal layer and N stands for the ordinary refractive index of the crystal layer.

If one neglects the spectral variation of the difference in the refractive index of the crystal for a first approximation, one can see one that the phase anisotropy varies essentially inversely with the wavelength and that for each crystal thickness the curve for the phase anisotropy as a function of the wavelength takes the form of a hyperbola.

The graph in FIG. 3 shows, in dashed lines, a network of curves, as is the case for different quartz platelets Thickness results.

From the graphical representations in Fig. 3 you can see first, that in order to achieve a compensation of the phase anisotropy that is valid for the entire spectral range under consideration for a com-

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bination of a mirror and a crystal layer is required that the curves for the phase differences at the mirror and on of the crystal layer are as symmetrical to the abscissa axis as possible. If the layer thickness for that deposited on the mirror Silica exceeds 400 A, or more generally when the optical thickness (the product of the geometrical Thickness and the refractive index) of the layer exceeds a value of 600 A, takes the curve belonging to the mirror in 3 shows such a shape that the compensation cannot be achieved over the entire spectral range of visible light. This is the same result as above for a usual one Mirror made of aluminum is indicated, which is coated with a layer of silicon dioxide of 1020 Å thick.

The examples described below allow a better one Understanding of the determination method for the combination of a mirror and a crystal layer to achieve an improved Correction of the phase anisotropy taking into account the requirement for sufficient mechanical strength of the respective Mirrors.

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235A5S2

example 1

It becomes an uncoated mirror made of aluminum, so a Mirror used without dielectric coating. The table in Fig. 4 In its first line it contains the results of such a mirror for an angle of incidence of 45 in the entire spectrum of visible light introduced phase anisotropy in degrees. You then look for the thickness for a quartz layer, which leads to an exact correction for the mean wavelength of about 5500 A for the spectral range of the visible Light leads. The second line of the table in FIG. 4 again indicates, in degrees, the phase anisotropy caused by a quartz plate a thickness of 2.17 microns, and the third row of the table in Fig. 4 contains the residual for the compensation, i.e. the phase difference that occurs after the light is reflected on the mirror and its passage through the quartz plate remains.

The values given in the third line of the table in FIG show that the residual for the compensation remains very small over the entire range of the spectrum of visible light. Of the the maximum error is only 0.86 for the red end of the Spectrum, which corresponds to an optical path of λ / 420.

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The residual for the compensation varies with the angle of incidence, it should be noted, however, that it always remains very small. In the graph of Fig. 5 are for the entire range of the spectrum of visible light, in turn, the values in degrees for the residual remaining in the compensation for an equal Combination of an uncoated mirror made of aluminum and a compensation layer made of quartz, 2.17 microns thick for different angles of incidence "between 22, 30 'and 60 are shown.

The lower the difference in the refractive indices, the better the compensation. Crystal as a function of wavelength varies. For this reason, magnesium fluoride proves to be even more suitable as a compensation material than quartz, and in both of them the last lines of the table of FIG. 4 are, on the one hand, the through phase anisotropy introduced by a magnesium fluoride platelet with a thickness of 1.68 microns, which leads to an accurate correction for a Mirror made of uncoated aluminum at the medium wavelength of the spectrum of visible light, and to the other the residual after this compensation is given. It can be seen that this residue turns out to be even smaller than for the one above treated case of a compensation by means of quartz.

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Certainly the use of a mirror made of uncoated aluminum is a delicate matter and it demands special Take precautions, especially when inserting the mirror in its holder and cleaning it. ·

Example 2

This example is illustrated in the table in Figure 6 and relates to an uncoated silver mirror with no dielectric Protective layer. As in the example described above, the thickness D = 3.92 microns for the quartz plate becomes so determines that there is an exact compensation for the mean wavelength of the spectral range of visible light. the The third line of the table in FIG. 6 again gives the residuals in degrees for compensation. One can see from the values given there that the material for the mirror is aluminum, silver This is preferable because the end result of silver has larger residuals for compensation than the one discussed above Example of a mirror made of uncoated aluminum can be obtained.

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Example 3

This example is illustrated in the first part of the table in Fig. 7, and it relates to a mirror made of aluminum covered with a protective layer of silicon dioxide with a thickness of 150 A is coated, which corresponds to an optical thickness of 220 A. Again, the residuals that result from a compensation by combining this mirror with a quartz plate of 3.39 microns thick. The numerical values given show that the residuals remaining after compensation are greater than in the embodiment 1, but they still remain in one an acceptable order of magnitude for numerous applications.

Example 4

This exemplary embodiment is shown in the second part of the table in Figure 7 illustrates and for the same conditions as before are the residuals, given for a compensation that turn out to be the Result of a combination of one with a layer of silicon dioxide 300 A thick (optical thickness 440 A) coated aluminum

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mirror obtained with a quartz plate 4.45 microns thick leaves.

The numerical values given show that the residuals in the compensation become larger when the thickness of the protective layer is off Silicon dioxide increases. The final choice of the thickness of this protective layer will therefore be appropriate depending on the prevailing ones Requirements for the intended use in question. If the remaining phase anisotropy for the combination of mirror and compensation plate is as small as possible want to make, one must accept a limitation to very small values for the thickness of the protective layer and possibly even completely uncoated mirrors work, which creates special conditions for mounting the mirror in the respective optical device brings. If, on the other hand, the mechanical strength of the mirror is the determining element, the minimum thickness for the dielectric protective layer to be applied is determined, then the thickness for the compensation layer made of quartz is determined, and from this one can then derive the corresponding residuals for the compensation.

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The above considerations have been presented in detail to better illustrate the method of operation. In practice all these calculations can be carried out easily and quickly using a computer.

Of course, the invention is not strictly limited to the specified * NEN exemplary embodiments are limited, rather it also extends to all equivalent embodiments. So you can, for example instead of crystalline platelets, which cannot be produced in the required thickness, with compensators of the Babinet design Soleil work that can be adjusted in a suitable way. In addition, although the above-described explanations can be used with games limit themselves to the correction for a single mirror, several mirrors with the help of a single compensation ■ compensate shift; in this latter case the thickness of the crystalline compensation layer must be multiplied by the number of mirrors and the same applies to the residual in compensation. '

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Claims (5)

-22- 235A562 claims 1. A method for determining an optically isotropic reflection arrangement that is to work with polarized light in an extended spectral range with good correction of the phase anisotropy and has at least one metallic mirror, which is optionally coated with a thin layer of a transparent dielectric and the one equivalent to it Crystalline compensation layer .assigned, dadurcii that for a given angle of incidence the thickness of the dielectric layer of the mirror or mirrors and the thickness of the crystalline compensation layer, one as a function of the other is determined by firstly the variation of the phase difference between the complex reflection coefficient the mirror or mirrors for light polarized parallel and perpendicular to the plane of incidence with different thicknesses of the dielectric depending on the wavelength in the respective spectral range, secondly the variation of the two polaris ation directions from the passage of the light through the compensation layer resulting phase difference for different thicknesses of the compensation layer as a function of the same 409823/072 2 Wavelengths and finally the variation of the residual in the compensation the phase differences as a function of the same wavelengths for each pair of a compensation layer of certain thickness and a mirror dielectric of certain thickness calculated in such a way that the respective phase differences for the mean wavelength of the relevant spectral range are equal to each other in absolute value and opposite in sign, and the final selection of the Thickness pair taking into account the minimum thickness for the dielectric, which is compatible with the mechanical strength of the mirror is, as the prevailing factor or taking into account the compensation residual when hits the mirror used allow corresponding thicknesses for the dielectric. 2 J reflection arrangement with isotropic oblique reflection with at least one metallic mirror, optionally coated with a thin layer of a transparent dielectric, to which a crystalline compensation layer equivalent to a thin layer is assigned, characterized in that the thickness of the dielectric layer of the mirror or mirrors and the thickness of the crystalline compensation layer are determined by the method of claim 1. 409823/07 22 ^ 3. Reflection arrangement according to claim 2, whose mirror made of aluminum and whose crystalline compensation layer made of quartz or consists of magnesium fluoride, characterized in that that the dielectric layer has an optical thickness of less than 600 Å. 4. Reflection arrangement with isotropic oblique reflection for below 45 incident white polarized light with a mirror made of aluminum, to which an equivalent compensation layer made of quartz is assigned, characterized in that the Aluminum mirror is uncoated and the thickness of the equivalent Grain pens ation layer is 2.2 microns. 5. Reflection arrangement with isotropic oblique reflection for incident polarized light below 45 with a mirror made of aluminum, which is assigned an equivalent compensation layer made of magnesium fluoride, characterized in that the Aluminum mirror is uncoated and the thickness of the equivalent Compensation layer is 1.7 microns. 409823/0722